Xn is a discrete-time Markov chain with state-space {1,2,3}, transition matrix, P = .2 .1 .7...

Xn is a discrete-time Markov chain with state-space {1,2,3}, transition matrix, P =

.2	.1	.7
.3	.3	.4
.6	.3	.1

a) find E[X1|X0=2] =

b) The P(X9=1|X7=3) =

C) The P(X2=2) =

Solutions

Expert Solution

.a)

E(X1/X0=2) = 1* P(X1=1/X0=2) + 2* P(X1=2/X0=2) + 3* P(X1=3/X0=2)
from the transition matrix, we know that
P(X1=1/X0=2) = 0.3
P(X1=2/X0=2) = 0.3
P(X1=3/X0=2) = 0.4
E(X1/X0=2) = 0.3+ 0.6+ 1.2 = 2.1

orchestra answered 1 year ago

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